Inclusion Criteria:

* Pathological confirmation of AML as defined by histologic, morphologic, or cytological evidence/confirmation of \>= 20% blasts in bone marrow aspirate and/or biopsy
* Must meet criteria for t-AML or AML with MRC as defined by the 5th Edition of the World Health Organization (WHO) Classification of Myeloid Neoplasms or the International Consensus Classification (ICC) of Myeloid Neoplasms. Patients must meet one of the following criteria:

* Therapy-related AML (AML derived from prior chemotherapy or radiation therapy)
* AML originating from prior hematologic malignancy (MDS, CMML, or MPN)
* AML with myelodysplasia-related cytogenetic abnormalities:

* One of the following cytogenetic abnormalities:

* Complex karyotype (3 or more unrelated chromosomal abnormalities in the absence of other class-defining recurrent genetic abnormalities as defined by WHO or ICC)
* -7/del(7q)
* Del(5q)/t(5q)/add(5q)
* +8
* i(17q)
* -17/add(17p) or del(17p)
* Del(20q)
* -13/del(13q)
* Del(11q)
* Del(12p)/t(12p)/add(12p)
* idicX(q13)
* AML with myelodysplasia-related mutations: Must have a mutation in one of the following genes:

* ASXL1
* BCOR
* EZH2
* RUNX1
* SF3B1
* SRSF2
* STAG2
* U2AF1
* ZRSR2
* No prior treatment for AML other than cytoreductive doses of hydroxyurea or leukapheresis
* Age \>= 18 and =\< 75 years on day of signing informed consent are eligible who are planned for intensive chemotherapy. Because no dosing or adverse event data are currently available on the use of pomalidomide in combination with daunorubicin and cytarabine liposome in patients \< 18 years of age, children are excluded from this study. Patients \> 75 years are not candidates for intensive chemotherapy with daunorubicin and cytarabine liposome
* Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 (Karnofsky \>= 60%)
* Total bilirubin =\< 1.5 institutional upper limit of normal (ULN) unless due to leukemic infiltration, Gilbert's Syndrome, or hemolysis
* Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 5 x institutional ULN
* Creatinine \>= 30 ml/min creatinine clearance by Cockcroft-gault
* Left ventricular ejection fraction (LVEF) \>= 50%
* Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial
* For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated
* Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured with undetectable HCV viral load. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load
* Patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, should have a clinical risk assessment of cardiac function using the New York Heart Association Functional Classification. To be eligible for this trial, patients should be class 2B or better
* Females of childbearing potential (FCBP), defined as a female who: 1) has reached menarche at some point, 2) has not undergone a hysterectomy or bilateral oophorectomy; or 3) has not been naturally postmenopausal for at least 24 consecutive months (i.e., has had menses at any time in the preceding 24 consecutive months) must have a negative pregnancy test 72 hours prior to the start of study therapy. For FCBPs in Arm A, they must have a negative serum or urine pregnancy test with a sensitivity of at least 25 mIU/mL within 10 - 14 days prior to and again within 24 hours of starting pomalidomide and must either commit to continued abstinence from heterosexual intercourse or begin TWO acceptable methods of birth control, one highly effective method and one additional effective method AT THE SAME TIME, at least 28 days before starting pomalidomide. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a vasectomy. All patients must be counseled at a minimum of every 28 days about pregnancy precautions and risks of fetal exposure
* Ability to understand and the willingness to sign a written informed consent document. Participants with impaired decision-making capacity (IDMC) who have a legally-authorized representative (LAR) and/or family member available will also be eligible

Exclusion Criteria:

* Patients with Wilson's Disease or Copper-related metabolic disorders
* Absolute blast count \> 30 x 10\^9/L (cytoreduction with leukapheresis or hydroxyurea can be used to achieve absolute blast count \< 30 x 10\^9/L prior to day 1 of treatment)
* Cumulative daunorubicin lifetime exposure \> 330 mg/m\^2 and \> 180 mg/m\^2 with prior mediastinal radiation therapy
* Patients with known active central nervous system leukemia should be excluded from this clinical trial because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. Patients receiving intrathecal chemotherapy prophylaxis should receive pomalidomide \>= 3 days after administration
* Patients with uncontrolled intercurrent illness including, but not limited to, active and uncontrolled infection, symptomatic congestive heart failure, unstable angina pectoris, and cardiac arrhythmia. Patients with infection under active treatment and controlled with antibiotics are eligible
* Known additional malignancy (with the exception of prior hematologic malignancies that have transformed to AML) that is active and/or progressive requiring treatment; exceptions include basal cell or squamous cell skin cancer, in situ cervical cancer or patients receiving maintenance treatments without active disease (for example, hormonal therapy for breast cancer or prostate cancer or other adjuvant chemotherapy approaches). Anti-cancer therapy as above should be discontinued \> 72 hours prior to day 1 of treatment
* Patients with psychiatric illness/social situations that would limit compliance with study requirements
* Receipt of prior allogeneic stem cell transplant
* Administration of any therapy for MDS, CMML, or MPN (conventional or unconventional) must be completed by 2 weeks prior to treatment with daunorubicin and cytarabine liposome. Use of strong CYP1A2 inhibitors should be avoided
* Patients who are receiving any other investigational agents
* History of allergic reactions attributed to compounds of similar chemical or biologic composition to pomalidomide (e.g. lenalidomide, thalidomide) or daunorubicin and cytarabine liposome or their excipients
* Development of erythema nodosum if characterized by a desquamating rash while taking thalidomide, lenalidomide, or similar drugs in the past
* Pregnant women are excluded from this study because pomalidomide is an immunomodulatory agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with pomalidomide, breastfeeding should be discontinued if the mother is treated with pomalidomide. These potential risks may also apply to other agents used in this study. Women of childbearing potential must be willing to undergo pregnancy testing
* Any other medical condition that in the opinion of investigator would place patient at increased risk for toxicity during pomalidomide treatment (i.e. history of recurrent or serious thromboembolic events such as massive pulmonary embolism)